Strings; Existing in One Dimension

[Realitycheck]

Can you give an example of any real physical thing that only has one dimension?

 

Your answer of "just by being" does not answer the question. It begs the question-- Just by being what?

 

You could also get into the dynamics of the measuring. Say you have a rectangle that is 1 meter wide and 1 mm high. If you are looking at it 1-dimensionally, it could easily be said that it is just 1 mm. The width would be irrelevant. It is a 1 mm object. The defining character of the object is derived by preset parameters which you define.

[kaneda]

So far not the slightest evidence that any more than 3 physical dimensions exist. I debated a one dimensional string with someone working on strings and he just didn't get the obvious properties of such a string. A one dimensional string cannot bend. It requires a second dimension at least to bend. It also means that there is no way they can join with each other. Strings have to have at least two dimensions to be fully functional, though they could join with one dimensional strings but would end up as little more than "spacers".

[Eric 5]

I described a possible vacuum physics state where light and matter waves do not travel "sideways" . In the interior, nearer to the event horizon of a black hole, the construction of transverse (sideways on a sphere) waves is strongly absorbing, not propagating. This is like curled-up dimensions, no?

 

Norman, lets keep this simple. Do you believe that dimensions, any dimension you want, are real physical things? If so, please explain what these dimensions are made of. I have read many books on string theory and not one author of these book has stated the physical properties of any dimension, and that includes the first three spatial dimensions that we are familiar with.

[Norman Albers]

Duh. HELLO? I'm talking radial spaghetti sticks. (of energy)

[Eric 5]

Which dimension is a radial spaghetti stick? Energy in what form? Is this energy a flow (moving) or a solid (condensed)?

[Norman Albers]

This reading of the equations of the Schwarzschild description says radially propagating light waves are allowed but that perpendicular to that, namely transverse movements in "lattitude and longitude" are not supported by the normal vacuum situation of c-squared being positive. It is negative and this signifies absorption in these directions, so these modes are not happening. Nearer to the center this changes, but toward the event horizon (we are talking interiors) it is arbitrarily strong.

[kaneda]

I tend to think of strings as bends in space. The problem I have with them is their size; that they are too small to affect or make anything on any scale we know. Now if they were 10-100 times smaller than an electron, they could maybe work together somehow to form all atomic particles and forces.

[Klaynos]

Why does size matter? The fundamental particles are TINY and yet they 'work together' to create the world around us, surely if we where to consider a 'constitute particle' for these fundamental particles it'd be even smaller?

[Norman Albers]

Our physics seems to melt down around the Planck length, no? This, even though the scale is roughly 10^-34 meters, while the Schwarzschild radius of an electron is about 10^-57 m. (Nice 'sup's', Klaynos)

[Eric 5]

Originally Posted by Norman Albers

I described a possible vacuum physics state where light and matter waves do not travel "sideways" . In the interior, nearer to the event horizon of a black hole, the construction of transverse (sideways on a sphere) waves is strongly absorbing, not propagating. This is like curled-up dimensions, no?

 

Norman, lets keep this simple. Do you believe that dimensions, any dimension you want, are real physical things? If so, please explain what these dimensions are made of. I have read many books on string theory and not one author of these book has stated the physical properties of any dimension, and that includes the first three spatial dimensions that we are familiar with.

 

Duh. HELLO? I'm talking radial spaghetti sticks. (of energy)

 

 

 

Which dimension is a radial spaghetti stick? Energy in what form? Is this energy a flow (moving) or a solid (condensed)?

[foodchain]

Duh. HELLO? I'm talking radial spaghetti sticks. (of energy)

 

If I get it you mean that dimensions are just abstractions to be used in mathematical frameworks to describe the natural world?

[Riogho]

So far not the slightest evidence that any more than 3 physical dimensions exist. I debated a one dimensional string with someone working on strings and he just didn't get the obvious properties of such a string. A one dimensional string cannot bend. It requires a second dimension at least to bend. It also means that there is no way they can join with each other. Strings have to have at least two dimensions to be fully functional, though they could join with one dimensional strings but would end up as little more than "spacers".

 

You can have a one-dimensional object bending in 3 dimensional space.

[Eric 5]

I can give you an example of a 1D object, a semiconductor quantum wire, I can even give you an example of a 0D object, in this case what we talk about as being 0D is the electron constriction, and is actually 0D.

 

 

 

 

This information can be found on wikipedia regarding quantum wire and nanotubes. Quantum wire conduct electrons. Quantum wire is made of nanotubes. Nanotubes are cylindrical. Cylindrical means it is 3D. So your quantum wire is 3D.

 

 

As for your 0D object, electrons are spherical, in order for an object to constrict a sphere it would have to be 3D. If anything is a physical object it is made of electrons. Electrons are 3D, so all objects would be 3D.

 

Is there any particular reason why something should not exist in one dimension?

 

This something? Give an example.

[Klaynos]

This information can be found on wikipedia regarding quantum wire and nanotubes. Quantum wire conduct electrons. Quantum wire is made of nanotubes. Nanotubes are cylindrical. Cylindrical means it is 3D. So your quantum wire is 3D.

 

 

As for your 0D object, electrons are spherical, in order for an object to constrict a sphere it would have to be 3D. If anything is a physical object it is made of electrons. Electrons are 3D, so all objects would be 3D.

 

Ok, the electron confinement is 1D in nanowires... in quantum dots, it is 0D confinement, these are 1D or 0D objects...

 

'electrons are spherical' I'm sorry but this shows a clear and basic misunderstanding of quantum mechanics, and therefore I wonder how you feel justified in making any claims about this kind of thing?

 

If you where asking questions fine, but you are just making statements which are clearly (to anyone with an understanding of the science) wrong.

[Norman Albers]

Electrons have a spherically symmetric electric field but they are not little balls.

[YT2095]

Bloody hell! Norman Albers made a post that Actually makes sense

 

I Must mark this on the Calendar!

[Norman Albers]

I wrote the transverse speed of light (in external coordinates) is [math]c_{trans} =c\sqrt{1-2m/r} [/math]. Outside the radius 2m the argument of the root is positive but heading toward zero smoothly. Below zero, the argument is negative and so the root is imaginary with small, increasing magnitude going inward. I can view the wave picture by writing a transverse sort of light propagation as: [math] e^{i\omega(\frac x c -t)}[/math] where x refers to the direction we are considering. Now consider the entry for c to be the reduced [math]c_{trans}[/math]. In the denominator this makes a larger and larger term multiplying x like a higher k, shorter waves. When it is imaginary, this effective length becomes the absorption characteristic in exponential falloff, sideways. We're talking thinnest vermicelli sticks just inside, then straight spaghetti for a ways. Somewhere on down, we get back to rotini.

[Sayonara]

This information can be found on wikipedia regarding quantum wire and nanotubes. Quantum wire conduct electrons. Quantum wire is made of nanotubes. Nanotubes are cylindrical. Cylindrical means it is 3D. So your quantum wire is 3D.

...

This something? Give an example.

No. Quantum wires CAN be made out of nanotubes, but they are not all manufactured so. A quantum wire is named for its transport properties, not for being 1-dimensional. Although the Wikipedia entry is hardly a good physics source, all of that is perfectly evident from reading it.

 

The particular wires Klaynos referred to are manufactured from gallium arsenide. They have physical diameter, but meet the requirements for a 1D object because the diameter is roughly the DeBroglie wavelength of an electron in that wire. Of course, whether or not you agree with the physicists working in this area is up to you, but personally I'd tend to respect their expertise.

See this article: http://physicsworld.com/cws/article/news/5013

 

It might help to separate the notion of a dimensionally restricted object, in or across which nothing can move in particular directions, from the notion of a mathematically ideal spatial dimensionality which is so infinitesimally small as to be non-existent.

 

I am not sure but it also appears you may be confusing the dimensionality of the object with the n-space it resides in.

[Norman Albers]

I am not convinced by intoning, timelike intervals are here spacelike, and spacelike intervals are timelike so that we can carry on with physics as usual locally, in a an interior. We are not in Kansas and should know this from the extreme light show we got "coming in". I am suggesting a basic phase change in the nature of space, as being a useful interpretation from the outside at least. Al dente. When I talk of 'spaghetti sticks' above I refer to the allowed radial, in and out WRT the center, modes. They are not square-root, but first-power.

[Eric 5]

Ok, the electron confinement is 1D in nanowires... in quantum dots, it is 0D confinement, these are 1D or 0D objects...

 

'electrons are spherical' I'm sorry but this shows a clear and basic misunderstanding of quantum mechanics, and therefore I wonder how you feel justified in making any claims about this kind of thing?

 

If you where asking questions fine, but you are just making statements which are clearly (to anyone with an understanding of the science) wrong.

 

O.K. I am willing to learn. Since I was unfamiliar with the terms: electron confinement and quantum dots, I looked up these terms on wikipedia and found the following:

 

Quantum dot

From Wikipedia, the free encyclopedia

 

"A quantum dot is a semiconductor whose excitons are confined in all three spatial dimensions. As a result, they have properties that are between those of bulk semiconductors and those of discrete molecules.

Researchers have studied quantum dots in transistors, solar cells, LEDs, and diode lasers. They have also investigated quantum dots as agents for medical imaging and hope to use them as qubits. Some quantum dots are commercially available."

 

 

Unless I have misread this, it seems that a quantum dot is a semiconductor.

 

 

Semiconductor

From Wikipedia, the free encyclopedia

 

"A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically.[1] Semiconductors are tremendously important in technology. Semiconductor devices, electronic components made of semiconductor materials, are essential in modern electrical devices. Examples range from computers to cellular phones to digital audio players. Silicon is used to create most semiconductors commercially, but dozens of other materials are used as well."

 

 

 

I looked up electron confinement on wikipedia and other reference books that I have on hand and did not find such a term, but I did find quantum confinement. I know this is not electron confinement, so if you have a definition for electron confinement then by all means let me know. Anyway, this is the definition for quantum confinement per wikipedia.

 

Quantum Confinement in Semiconductors:

 

"In an unconfined (bulk) semiconductor, an electron-hole pair is typically bound within a characteristic length called the Bohr exciton radius. If the electron and hole are constrained further, then the semiconductor's properties change. This effect is a form of quantum confinement, and it is a key feature in many emerging electronic structures.

Other quantum confined semiconductors include:

 

quantum wires, which confine the motion of electrons or holes in two spatial dimensions and allow free propagation in the third.

 

quantum wells, which confine the motion of electrons or holes in one dimension and allow free propagation in two dimensions."

 

 

This definition states that quantum confinement is an action or state of being of an electron or hole that can occur in a semiconductor under special conditions. It defines how an electron or (electron) hole is managed under these certain conditions.

 

So in this definition quantum confinement is not describing an object.

 

For those of you who do not know what an electron hole is you should look up the term for yourself to get a full understanding. But I will give the definition that wikipedia gave.

 

Hole

From Wikipedia, the free encyclopedia

 

"Electron hole, in physics and electronics, the absence of an electron in the valence band."

 

 

As far as the definition for electron, this is a basic definition from wikipedia.

 

 

Electron

From Wikipedia, the free encyclopedia

 

"The electron is a fundamental subatomic particle that carries a negative electric charge. It is a spin ½ lepton that participates in electromagnetic interactions, its mass is approximately 1 / 1836 of the proton. Together with atomic nuclei (protons and neutrons), electrons make up atoms. Their interaction with adjacent nuclei is the main cause of chemical bonding."

 

 

Subatomic particle

From Wikipedia, the free encyclopedia

 

"A subatomic particle is an elementary or composite particle smaller than an atom. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic matter.

Subatomic particles include the atomic constituents electrons, protons, and neutrons. Protons and neutrons are composite particles, consisting of quarks. A proton contains two up quarks and one down quark, while a neutron consists of one up quark and two down quarks; the quarks are held together in the nucleus by gluons. There are six different types of quark in all ('up', 'down', 'bottom', 'top', 'strange', and 'charm'), as well as other particles including photons and neutrinos which are produced copiously in the sun. Most of the particles that have been discovered are encountered in cosmic rays interacting with matter and are produced by scattering processes in particle accelerators. There are dozens of subatomic particles."

 

 

As far as electrons being spherical, I personally have never seen an electron up close, but all diagrams and picture representations that I have seen of an electron were spherical. Please let me know of a better representation of an electron if there is one.

 

 

 

In case you were curious as to what a particle is:

 

particle

[edit] Etymology

 

From Latin particula ‘small part, particle’, diminutive of pars ‘part, piece’.

[edit] Noun

particle (plural particles)

 

A body with very small size; a fragment.

(physics) An elementary particle or subatomic particle.

(linguistics) A word that has a particular grammatical function but does not obviously belong to any particular part of speech, such as the word to in English infinitives.

 

 

This is by no means a complete definition of particle, so for a complete understanding of the term particle please grab your dictionary.

 

 

But anyways, if there is a different definition for electron according to quantum mechanics, please inform me.

 

Like I stated at the beginning of this post I am willing to learn more.

 

As far as a 1D or 0D object existing, I did not see evidence of such an object from the two terms that you presented (electron confinement and quantum dots) If there is an object that is only 1D or 0D, I have not come across such an object in my studies. I am always trying to understand more of the world around me, so if you have any reference to a 1D or 0D object please let me know. Thank you.

 

P.S I looked up the word object in a dictionary and could not see how any object could only be 1D or 0D. In fact, I defined the word zero (0) and the word dimension.... well you try and explain how this could be an object. 0D object is a contradiction of terms.

[Klaynos]

O.K. I am willing to learn. Since I was unfamiliar with the terms: electron confinement and quantum dots, I looked up these terms on wikipedia and found the following:

 

Quantum dot

From Wikipedia, the free encyclopedia

 

"A quantum dot is a semiconductor whose excitons are confined in all three spatial dimensions. As a result, they have properties that are between those of bulk semiconductors and those of discrete molecules.

Researchers have studied quantum dots in transistors, solar cells, LEDs, and diode lasers. They have also investigated quantum dots as agents for medical imaging and hope to use them as qubits. Some quantum dots are commercially available."

 

 

Unless I have misread this, it seems that a quantum dot is a semiconductor.

 

They are made out of semiconductor materials, in the same way a tire is made out of rubber. When talking about such small objects the properties they have changes considerably with their shape.

 

 

Semiconductor

From Wikipedia, the free encyclopedia

 

"A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically.[1] Semiconductors are tremendously important in technology. Semiconductor devices, electronic components made of semiconductor materials, are essential in modern electrical devices. Examples range from computers to cellular phones to digital audio players. Silicon is used to create most semiconductors commercially, but dozens of other materials are used as well."

 

 

 

I looked up electron confinement on wikipedia and other reference books that I have on hand and did not find such a term, but I did find quantum confinement. I know this is not electron confinement, so if you have a definition for electron confinement then by all means let me know. Anyway, this is the definition for quantum confinement per wikipedia.

 

 

The two are exchangeable.

 

 

Quantum Confinement in Semiconductors:

 

"In an unconfined (bulk) semiconductor, an electron-hole pair is typically bound within a characteristic length called the Bohr exciton radius. If the electron and hole are constrained further, then the semiconductor's properties change. This effect is a form of quantum confinement, and it is a key feature in many emerging electronic structures.

Other quantum confined semiconductors include:

 

quantum wires, which confine the motion of electrons or holes in two spatial dimensions and allow free propagation in the third.

 

quantum wells, which confine the motion of electrons or holes in one dimension and allow free propagation in two dimensions."

 

 

This definition states that quantum confinement is an action or state of being of an electron or hole that can occur in a semiconductor under special conditions. It defines how an electron or (electron) hole is managed under these certain conditions.

 

If you confine one dimension you restrict the electron from being able to use that dimension, the electron doesn't 'know' the confined dimension exists.

 

Wells are 2D, wires 1D and dots 0D.

 

So in this definition quantum confinement is not describing an object.

 

The electron is the object the confinement is removing it's dimensions.

 

For those of you who do not know what an electron hole is you should look up the term for yourself to get a full understanding. But I will give the definition that wikipedia gave.

 

Hole

From Wikipedia, the free encyclopedia

 

"Electron hole, in physics and electronics, the absence of an electron in the valence band."

 

 

As far as the definition for electron, this is a basic definition from wikipedia.

 

 

I don't really like that description, they are psydoparticles and it is as valid to talk about them in solid state physics as it is to talk about electrons.

 

 

Electron

From Wikipedia, the free encyclopedia

 

"The electron is a fundamental subatomic particle that carries a negative electric charge. It is a spin ½ lepton that participates in electromagnetic interactions, its mass is approximately 1 / 1836 of the proton. Together with atomic nuclei (protons and neutrons), electrons make up atoms. Their interaction with adjacent nuclei is the main cause of chemical bonding."

 

 

Subatomic particle

From Wikipedia, the free encyclopedia

 

"A subatomic particle is an elementary or composite particle smaller than an atom. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic matter.

Subatomic particles include the atomic constituents electrons, protons, and neutrons. Protons and neutrons are composite particles, consisting of quarks. A proton contains two up quarks and one down quark, while a neutron consists of one up quark and two down quarks; the quarks are held together in the nucleus by gluons. There are six different types of quark in all ('up', 'down', 'bottom', 'top', 'strange', and 'charm'), as well as other particles including photons and neutrinos which are produced copiously in the sun. Most of the particles that have been discovered are encountered in cosmic rays interacting with matter and are produced by scattering processes in particle accelerators. There are dozens of subatomic particles."

 

 

As far as electrons being spherical, I personally have never seen an electron up close, but all diagrams and picture representations that I have seen of an electron were spherical. Please let me know of a better representation of an electron if there is one.

 

 

You can't see them up close, it's not fundamentally possible. They're not really particles, but a wave and a particle. You can't apply an accurate classical picture of one... In free space when not affected by an external E or B field their E field is spherically symmetric.

 

 

In case you were curious as to what a particle is:

 

particle

[edit] Etymology

 

From Latin particula ‘small part, particle’, diminutive of pars ‘part, piece’.

[edit] Noun

particle (plural particles)

 

A body with very small size; a fragment.

(physics) An elementary particle or subatomic particle.

(linguistics) A word that has a particular grammatical function but does not obviously belong to any particular part of speech, such as the word to in English infinitives.

 

 

This is by no means a complete definition of particle, so for a complete understanding of the term particle please grab your dictionary.

 

As none of the definitions here are, wp is good for a basic understanding but it is far from perfect.

 

 

But anyways, if there is a different definition for electron according to quantum mechanics, please inform me.

 

Look up wave particle duality.

 

Like I stated at the beginning of this post I am willing to learn more.

 

As far as a 1D or 0D object existing, I did not see evidence of such an object from the two terms that you presented (electron confinement and quantum dots) If there is an object that is only 1D or 0D, I have not come across such an object in my studies. I am always trying to understand more of the world around me, so if you have any reference to a 1D or 0D object please let me know. Thank you.

 

P.S I looked up the word object in a dictionary and could not see how any object could only be 1D or 0D. In fact, I defined the word zero (0) and the word dimension.... well you try and explain how this could be an object. 0D object is a contradiction of terms.

 

You must remember that the dictionary definition and the definition used by scientists are often very different.

 

Some references:

 

[1] M. A. Reed et al, Phys. Rev. Lett. 60, 535, 1988

[2] Kouwenhoven & Marcus 'Quantum Dots' Physics World, 35 (June 1998)

[3] M. A. Reed, Sci. Am. 263 (5), 122 (1990)

[4] C. Weisbuch and B. Vinter, Quantum Semiconductor Structures: Fundamentals and

Applications [Academic Press, North-Holland, 1991] p. 21

[5] T. Chakraborty, Quantum dots : a survey of the properties of artificial atoms [Elsevier, North-

Holland, 1999]

[6] D. Leonard, K. Pond, and P. M. Petroff, Phys. Rev. B, 50, 11687, 1994

[7] N. N. Ledentsov et al, Semiconductors, 32, 343, 1997

[8] W. G. van der Wiel et al, Reviews of Modern Physics, 75, 1, 2003

[9] C. W. J. Beenakker, Phys. Rev. B, 44, 1646, 1990

[10] J. R. Guest et al, Phys. Rev. B, 65, 241310, 2002

[11] M. V. Artemyev et al, Phys. Stat. Sol. (b), 224, 393, 2001

[Sayonara]

As far as a 1D or 0D object existing, I did not see evidence of such an object from the two terms that you presented (electron confinement and quantum dots) If there is an object that is only 1D or 0D, I have not come across such an object in my studies. I am always trying to understand more of the world around me, so if you have any reference to a 1D or 0D object please let me know. Thank you.

You appear to have completely ignored my post.

 

P.S I looked up the word object in a dictionary and could not see how any object could only be 1D or 0D. In fact, I defined the word zero (0) and the word dimension.... well you try and explain how this could be an object. 0D object is a contradiction of terms.

The dictionary gives definitions for common usage. It is not a technical glossary

for physics.

[Eric 5]

You appear to have completely ignored my post.

 

 

The dictionary gives definitions for common usage. It is not a technical glossary

for physics.

 

 

Honestly, I had no intensions of appearing to have completely ignored your post. I just wanted to find out the meaning of these terms since I was unfamiliar with them. From the references that I used to define these terms I could not come to the conclusion that Electron Confinement and Quantum Dots are 1D or 0D objects or that it is physically possible for a 1D or 0D object to exist. I paid much attention to your post with the sole purpose of trying to learn something. So before this gets out of hand, if it is possible, can you point me to a reference that you are using that would show the definition of object and dimension that you are using to show that it is possible for a physical object to have only 1 or 0 (zero) dimensions. It is obvious that if I am using one set of definitions for these terms and you are actually using a different set of definitions we will never be on the same page and so never be able to rationally discuss this topic. Again, I apologize if I came across as totally ignoring your post, that was not my intension. I do want to learn more about this topic, as I am sure others are as well, so I am willing to cooperate, get involved and learn. So I would appreciate any help you or anyone on this post can give. You would not only be making things more clear for me, but would be clearing things up for anyone else who might misunderstand what you were really trying to say. Thank You.

[iNow]

So I would appreciate any help you or anyone on this post can give.

 

You do understand that you've already blanketly dismissed the answers already provided to these questions you've already asked, right?

[Klaynos]

Eric 5, I gave a list of good academic references above....